Helical reconstruction of VP39 reveals principles for baculovirus nucleocapsid assembly

Baculoviruses are insect-infecting pathogens with wide applications as biological pesticides, in vitro protein production vehicles and gene therapy tools. Its cylindrical nucleocapsid, which encapsulates and protects the circular double-stranded viral DNA encoding proteins for viral replication and entry, is formed by the highly conserved major capsid protein VP39. The mechanism for VP39 assembly remains unknown. We use electron cryomicroscopy to determine a 3.2 Å helical reconstruction of an infectious nucleocapsid of Autographa californica multiple nucleopolyhedrovirus, revealing how dimers of VP39 assemble into a 14-stranded helical tube. We show that VP39 comprises a distinct protein fold conserved across baculoviruses, which includes a Zinc finger domain and a stabilizing intra-dimer sling. Analysis of sample polymorphism shows that VP39 assembles in several closely-related helical geometries. This VP39 reconstruction reveals general principles for baculoviral nucleocapsid assembly.


Reviewer #2 (Remarks to the Author):
In their manuscript "Helical reconstrucfion of VP39 baculovirus nucleocapsid assembly reveals principles for baculovirus nucleocapsid assembly", the authors report the structure of the filament forming main component of the nucleocapsid, VP39, from Autographa californica mulfiple nucleopolyhedrosis virus.While the thorough analysis of the structural data and the link to known biological data are clear strengths of this manuscript, several image processing methodological points need to be addressed to validate all conclusions drawn by the authors.
Below a detailed review of the points of concern.

Major remarks:
A general comment is that the processing strategy chosen by the authors is unnecessarily complicated, and the interplay between different processing software (cisTEM, Cryosparc, Relion..) can be a source of problems, such as loss of useful data (such as the correspondence between filament IDs and segments, intersegment distances, etc..), or the observed arfifacts in the FSC curve (not dropping to zero).Based on the data descripfion and the difficulfies of this dataset, there is no clear jusfificafion (which could be added by the authors in the Method secfion) for choosing this processing strategy, rather than doing the enfire processing in Relion (or Cryosparc), that include all tools for helical refinement.
A.1/ In the "Data availability" secfion, the authors menfion that both the helical map and the local refinement map were deposited.However, in the PDB validafion report, we can only see the local refinement map, this should be fixed and a new report sent for review.Based on other abnormalifies in the validafion report (see below in the minor points), we kindly ask the authors to provide the half maps for further review.
A.2/ None of the half maps FSCs are dropping to zero.The authors jusfify that by "because of the semiindependent half map refinement as implemented in in cisTEM, the high degree of symmetry, and the relafively small masked volume compared to the total volume of the box, there likely is some inflafion of the curves".Based on the curve shapes, the inflafion is rather "certainly" than "likely", and the jusfificafions proposed by authors do not seem appropriate, and should be re-phrased, if not fixed (which is the preferred recommendafion, but the reviewer appreciate the amount of work for gefting a final structure that will look very similar to the presented one).First, for the curves corresponding to helical reconstrucfion in Extended Data Fig 2A, FSCs should be calculated between unsymmetrized half maps, as it is done in Relion or Cryosparc, not between symmetrized half maps.A mask containing only a small z porfion of the helix can be used to avoid including blurry edges of the unsymmetrized half maps in the FSC calculafion.For the helical reconstrucfion again, when converfing from cisTEM to Cryosparc or to Relion, if the correspondence between filaments IDs and segments is lost, or if the informafion on the distance between the segments from extracfion is lost, it is expected to get such strong arfifacts in the FSCs.To avoid that, re-extracfion should be done so that the respecfive software has all the necessary metadata on the segments, used to split the dataset appropriately, and to limit the Y search of each segment based on the intersegment distance, which are the likely reasons of the FSC curves not dropping.
For the local refinements (Extended Data Fig 2B), the authors used the symmetry expansion tool relion_parficle_symmetry_expand with the opfion --asu 3 (as stated in the method).Based on the extracfion parameters, the "asu" opfion should have been 1, otherwise there is data duplicafion which can be an addifional reason for the arfifactual FSC curves (on top of the reasons menfioned for the helical refinement).
The jusfificafions on "high degree of symmetry, and the relafively small masked volume" should be removed, since those properfies are present for many helical assemblies for which such arfifacts are not present.
A.3/ The analysis of the nucleocapsid polymorphism by a supervised classificafion approach, although interesfing and well thought -especially the reference preparafion part-, suffer from severe drawbacks that make it difficult to take the author's conclusions as granted.First the authors should provide evidence of the correctness of the different helical symmetry assignments : this shouldn't be difficult, since the classificafion provide them with different segment stacks and associated helical symmetry that could be used for refinement to provide high -or mediumresolufion maps corresponding to the the different helical symmetries.On top of validafing the classificafion procedure, this would allow the author to merge subtracted parficles from different diameter tubes, hence improving the resolufion of the local refinements and befter characterizing potenfial laftice deformafion (stretching, etc) by 3D classificafion or 3D variability analysis of the subtracted parficles.
Another simple analysis that would strengthen the approach, would be to show the orientafion distribufion (on-axis and out-of-plane angles), for some representafive references (e.g. the 5 most populated without flaftening).The distribufion is expected to be ~flat for on-axis angles, and gaussianshaped, centered on 0 (or 90 depending on the convenfion) for the out-of-plane angles, if the symmetry assignment is correct.If the first proposed approach (calculafing the 3D structures corresponding to the different helical symmetries) is beyond the scope of this work on author's point of view, then the authors should provide these plots for validafion.
For the flaftening, to be more conclusive, the authors could show the sum of power spectra of aligned segments corresponding to a parficular helical symmetry (e.g. the most abundant), for the least and the most flaftened classes.Effects of the flaftening should be visible by the stretching of the signal on the layer lines.
Lines 345-347, the authors state that "A closer inspecfion of the segments belonging to tubes with [n1=14, n2=14]-symmetry revealed that only approximately 14% of these segments aligned best to the non-flaftened 3D reference."Have the authors tried to run refinements before and after removing flaftened segments, e.g.keeping up to flaftening of 5%, and assess the improvements ?On one hand, this would validate the classificafion based on flaftening, and on the other hand integrate this classificafion procedure in their processing pipeline.
A.4/ Lines 572-587 : the authors describe a complicated protocol for refined helical reconstrucfion, instead of simply using relion_refine with the helical opfions .Could the authors explain why ?If the reason is the loss of metadata (priors on in-plane and out-of-plane, intersegment distance, filament IDs), then the authors should consider re-extracfing in Relion using the filament ends coordinates corresponding to their subset of selected segments.
B.2/ Lines 132-133 : "Our reconstrucfion reveals that individual VP39 subunits pack as dimers that assemble into 14 protofilaments".This is a general statement that does not apply to the enfire dataset, it should be more precisely phrased for the readers to understand that it also assembles in other number of protofilaments structures.B.3/ Line 532 : "with a search range of -15 ̊ to 15 , rise: 43.8 Å with a search range of 20-60 Å, C15".This should be C14.2A : "Power spectrum of a 2D class average, which has been symmetrized along its meridian".Instead of the PS of the 2D class average, it is recommended to use the sum of PS of the segments belonging to that class-average, which avoid some arfifacts present in the PS of class-averages, such as left/right asymmetry.No symmetrizafion should be necessary if the PS is not arfifactual.B.5/ Lines 315-316 : "potenfial symmetries (C12-C15) possible for the given Bessel orders idenfified during Fourier-Bessel analysis of several 2D class averages (Supplementary Fig. 2)."Supp Fig 2 shows only the analysis on one class, therefore the reader can not appreciate the validity of this statement and the differences in first Bessel peak posifion across the different structures (which might actually be compensated by diameter variafion).

B.4/ Supplementary Fig
B.6/ Lines 544-545 : "We determined inifial helical symmetry parameters by indexing the power spectra of these class averages using PyHI (Python v. 3.7)".It is not clear why this indexafion was done, since the authors already obtained helical parameters in previous steps.B.7/ For the local refinements, it should be stated whether refinement was done with C2 (or D1) symmetry, or only in C1.Since the symmetry expansion was done with C14 and not D14, we would recommend the authors to use the 2-fold symmetry for refinement.
B.8/ Validafion report, secfion 6.2.1/6.2.2 : While the "raw map" seem to have 2-fold cyclic symmetry, or at least have one of its axis (X) aligned with a (maybe imposed, see point B.7 to clarify) C2 symmetry axis, this is not the case for the "primary map".Why such a difference ?In the "raw map" central slices, can the author explain the very strong differences in areas with no protein density near the center and the areas with no protein density far from the center ?In other words, why is the noise appearance so different depending on the area of the volume ?It looks like a different low-pass filter had been applied in different areas, which seem odd for a "raw map".This is a potentially interesting structural study of the VP39 nucleocapsid.There are a number of minor issues, but the most major one is that there is no discussion of any relation between this structure and the viral genome.It is called a nucleocapsid for a reason.
We appreciate the reviewer's comment regarding discussing the relationship between the structure and viral genome packaging.We would like to point out that we write in the Discussion section: "The fold includes a Zn-finger (ZF) region with a Zn 2+ ion coordinated by a conserved CCCH motif, which is facing the capsid lumen.Moreover, it is surrounded by basic residues, priming this region as a possible binding pocket for the viral DNA."In the Results section, we describe that "The ZF faces the luminal volume of the VP39 nucleocapsid assembly and is surrounded by positively charged residues, consistent with a role in binding viral DNA (Fig. 2E; Extended Data Fig. 5, Extended Data Fig. 6)."While we can speculate as to the location of a potential DNA binding site, we are cautious in making any more claims without extensive experimental evidence.
We have now added the following sentence to the discussion: "The charge pattern across the luminal face of the nucleocapsid suggests a surface primed for interacting with multiple strands of packaged DNA (Extended Data Fig. 6)." The question of viral genome packaging into the nucleocapsid, while a very interesting question, is beyond the scope of our work.In our dataset and in unpublished negative stain micrographs, all tubes appeared to be empty.Investigating the interaction of the viral genome and the structure would require obtaining either fully packaged nucleocapsids before genome release, or nucleocapsids, which are in the process of being packaged with DNA.This requires catching the nucleocapsid in just the right time in its complex life cycle.We hope that the reviewer can appreciate that our structure-and especially our discovery of an inward-facing Zn-binding site in VP39-now opens new experimental avenues for investigating DNA binding and packaging into the nucleocapsid.
The abstract states that "Analysis of sample polymorphism revealed tube flattening could account for different helical geometries."But the paper states the exact opposite, such as: "Most of the remaining segments belonged to tubes of either C15 or C13 symmetry, which correspond to occasional insertions or deletions of single subunits in the helical plane.These differences in helical symmetries generate nucleocapsids that match the published range of AcMNPV diameters."and "which correspond to our observations of 13-to 15-start helices by indexing of segment 2D class averages (Extended Data Fig. 1, Supplementary Fig. 2)."Perhaps the abstract and text were written by two different people?Or the abstract was written before the analysis was done?
We thank the reviewer for pointing out that statements in the abstract and the main text regarding sample polymorphism appear contradictory.We updated the sentence in the abstract to "Analysis of sample polymorphism revealed that VP39 assembles in several closelyrelated helical geometries.
More minor issues: Lines 128-129) It is stated that the resolution of 4.0 Å was obtained by a map:model FSC.But in Methods, it is stated: "resulted in a map at about 4 Å resolution (3.3 Å FSC at 0.148 in CryoSPARC using half maps, 4.3 Å FSC at 0.5 map vs model".So what is stated in the text appears not to be true.Further, it is worth noting that the so-called "gold standard" map:map FSC is not really a gold standard, as shown by this example.It is stated in the legend to Extended Data Fig. 2 that the curves "do not strictly drop to zero" but this is misleading, as they simply do not drop to zero showing the artifactual correlation between the two half maps. As suggested by reviewer #2, we have now calculated new reconstructions from a segment particle stack with [n 1 =14, n 2 =14] symmetry after supervised classification (see below).We have also fixed an error in our code base that caused inflated correlation in the FSC curves calculated from half maps (there was a fraction of tubes that contributed some segments to both half maps); they do drop to zero now as would be excepted.Reviewer #1 is correct that the half map FSC curves are not "gold standard", because we used cisTEM for particle alignment, where the half maps are treated semi-independently, but where the resolution is limited to prevent alignment bias.
We have updated Extended Data Fig. 2 with the corrected FSC curves from the new reconstructions and refined model.The estimated nominal resolution from the half map analysis (3.6 Å for the helical reconstruction, 3.2 Å for the local reconstruction) is now in much better agreement with the values obtained from the full map to model analysis (4.0 Å for the helical reconstruction, 3.3 Å for the local reconstruction).
We updated the text in Methods to reflect the correct value of 4.0 Å FSC at 0.5 map vs model, as shown in Extended Data Fig. 2C: "Following one round of 3D classification (10 classes), in which we selected two classes with similar tube diameter and refined each class separately using the helical refinement option in CryoSPARC (twist: 7.5˚ with a search range of -15˚ to 15˚, rise: 44 Å with a search range of 20-60 Å, D14, non-uniform refinement option), a final helical refinement of the two combined classes (4,983 segments, twist: 7.5˚ with a search range of -15˚ to 15˚, rise: 44 Å with a search range of 20-60 Å, D14, non-uniform refinement option), resulted in a map at 4.1 Å resolution (0.143 FSC at 4.1 Å using half maps, 0.5 FSC at 4.4 Å using map and final model [see below]; Extended Data Fig. 2A and C)." Line 133) "spiral shape" is a poor description, as a spiral typically has a changing radius.It would be much better to simply refer to these as helical strands.
We updated the text in line 133 to "In our reconstruction, individual VP39 subunits pack as dimers that assemble into 14 helical strands and together form the central cylindrical structure of the baculoviral nucleocapsid (Fig. 1C)."Line 155) "each monomer".There are no monomers, which by definition are monomeric.This should be "each subunit" We updated the text in line 155 to "Each dimer subunit comprises a mixed alpha/beta fold, with extensive interdigitation of elements with its partner in the dimer (Fig. 2B, D)." Further, in the discussion, we changed the text to "The VP39 dimer subunit adopts a unique mixed alpha/beta fold (Fig. 2), which was not recognized by the DALI structural comparison server and Foldseek."Lines 396-397) "majority of the tubes (40% of the segments".A majority means > 50%! We updated the text in lines 396-397 to "We found that 40% of the tubes in our dataset assembled with [n 1 =14, n 2 =14] helical symmetry."Lines 401-403) "Our analysis furthermore indicated that most of the tubes were flattened in our preparation, which may be due to blotting during sample vitrification and the flexibility of the inter-dimer contacts."There is no explanation here how blotting could cause such flattening.What is more likely is that the large compressional forces arising from the thin film in which the tubes are embedded are responsible for the flattening.This has been described previously for axonemes (e.g., Bui et al., 2012, JCB 198: 913-925).
We thank the reviewer for raising this point.We agree that there is no explanation for how blotting could cause such flattening and we appreciate the provided reference for axonemes.We changed the sentence in lines 401-403 to: "Our analysis furthermore indicated that most of the tubes were flattened in our preparation.While we cannot unambiguously identify the source of flattening in our sample, it is noteworthy that tube flattening has been observed for cilia in published work 60 , with one study describing tube compression parallel to the ice plane on the EM grid 61 .
We updated the text in line 655 to "We limited the resolution for alignment to 12 Å (dictated by the available computational resources), imposed C1 symmetry, and used a spherical mask with an outer radius of 360 Å."

Reviewer #2 (Remarks to the Author):
In their manuscript "Helical reconstruction of VP39 baculovirus nucleocapsid assembly reveals principles for baculovirus nucleocapsid assembly", the authors report the structure of the filament forming main component of the nucleocapsid, VP39, from Autographa californica multiple nucleopolyhedrosis virus.While the thorough analysis of the structural data and the link to known biological data are clear strengths of this manuscript, several image processing methodological points need to be addressed to validate all conclusions drawn by the authors.Below a detailed review of the points of concern.

Major remarks:
A general comment is that the processing strategy chosen by the authors is unnecessarily complicated, and the interplay between different processing software (cisTEM, Cryosparc, Relion..) can be a source of problems, such as loss of useful data (such as the correspondence between filament IDs and segments, intersegment distances, etc..), or the observed artifacts in the FSC curve (not dropping to zero).Based on the data description and the difficulties of this dataset, there is no clear justification (which could be added by the authors in the Method section) for choosing this processing strategy, rather than doing the entire processing in Relion (or Cryosparc), that include all tools for helical refinement.
On the processing strategy: The complexity of this structure determination required the use of program tools from different software packages.We made sure that all metadata was carried froward when switching from one package to the other (including all the metadata associated with helical reconstructions, such as the filament ID, helical track length, and prior angles).We provide a detailed explanation in A.4 and we have further clarified the chosen processing strategy in the Methods section.

On the FSC curves:
We were able to fix an error in our code base that caused the observed artifacts in the FSC curves, and they drop to zero now as expected (see comment in A.2 below).
A.1/ In the "Data availability" section, the authors mention that both the helical map and the local refinement map were deposited.However, in the PDB validation report, we can only see the local refinement map, this should be fixed and a new report sent for review.Based on other abnormalities in the validation report (see below in the minor points), we kindly ask the authors to provide the half maps for further review.
As suggested below, we have now calculated new reconstructions from a segment particle stack with [n 1 =14, n 2 =14] symmetry after supervised classification (see below) and have deposited all relevant maps (helical and local reconstructions) together with the refined model.We are also happy to make all these files available for further review.They are the following: A.2/ None of the half maps FSCs are dropping to zero.The authors justify that by "because of the semi-independent half map refinement as implemented in in cisTEM, the high degree of symmetry, and the relatively small masked volume compared to the total volume of the box, there likely is some inflation of the curves".Based on the curve shapes, the inflation is rather "certainly" than "likely", and the justifications proposed by authors do not seem appropriate, and should be re-phrased, if not fixed (which is the preferred recommendation, but the reviewer appreciate the amount of work for getting a final structure that will look very similar to the presented one).First, for the curves corresponding to helical reconstruction in Extended Data Fig 2A, FSCs should be calculated between unsymmetrized half maps, as it is done in Relion or Cryosparc, not between symmetrized half maps.A mask containing only a small z portion of the helix can be used to avoid including blurry edges of the unsymmetrized half maps in the FSC calculation.
We are grateful that the reviewer pointed this out.We investigated and discovered an error in our code base that we have fixed now.Specifically, there was a fraction of tubes that contributed segments to both half maps, which lead to the observed inflation of the FSC curves.We have recalculated the FSC curves with the updated code and they do now drop to zero as can be seen in the revised Extended Data Fig. 2. The estimated resolution based on the half maps (3.6 Å for the helical reconstruction, 3.2 Å for the local reconstruction) is now also in agreement with the estimated resolution based on the correlation between the refined models and the final maps (4.0 Å for the helical reconstruction, 3.3 Å for the local reconstruction).Because we used cisTEM for particle alignment, where half maps are treated "semiindependently" and alignment bias is prevented by limiting the resolution for alignment, our analysis was not affected by this code error except for the final FSC calculation.We have removed the wrong explanation for the inflated FSC curves, which is now obsolete, from the manuscript.
To our knowledge, Relion and Cryosparc calculate FSC curves after symmetrization, we therefore believe it would not be helpful to add such plots to the manuscript.However, we have now deposited (and made available to the reviewer) the unmodified, unsymmetrized half maps that where reconstructed in C1.
For the helical reconstruction again, when converting from cisTEM to Cryosparc or to Relion, if the correspondence between filaments IDs and segments is lost, or if the information on the distance between the segments from extraction is lost, it is expected to get such strong artifacts in the FSCs.To avoid that, re-extraction should be done so that the respective software has all the necessary metadata on the segments, used to split the dataset appropriately, and to limit the Y search of each segment based on the intersegment distance, which are the likely reasons of the FSC curves not dropping.
We carried forward all metadata of each segment during data processing, including the filament IDs and relative extraction coordinates along the helical axis (helical track length).After fixing a code error, as explained in the comment above, the FSC curves drop normally.We did not limit the x and y shift during alignment of the helical segments.The plot shown here shows the distribution of the shifts along the helical axis after alignment for the final reconstruction: The mean shift was 0.03 Å with a standard deviation of 12.8 Å.The segment extraction spacing along the helical axis was 44.2 Å.This shows that, even though we did not limit the search range during alignment, the segments aligned locally at the extraction position.
For the local refinements (Extended Data Fig 2B ), the authors used the symmetry expansion tool relion_particle_symmetry_expand with the option --asu 3 (as stated in the method).Based on the extraction parameters, the "asu" option should have been 1, otherwise there is data duplication which can be an additional reason for the artifactual FSC curves (on top of the reasons mentioned for the helical refinement).
Data duplication within each half dataset should not inflate the FSC curves (and indeed they did drop to zero after we fixed our code error [see above]).But we have now calculated a new local reconstruction from the [n 1 =14, n 2 =14]-symmetry stack with the option --asu 1 (which corresponds to C14 symmetry expansion in this case here) as suggested by the reviewer.
The justifications on "high degree of symmetry, and the relatively small masked volume" should be removed, since those properties are present for many helical assemblies for which such artifacts are not present.
We have now removed this sentence from the manuscript.See comments above.
A.3/ The analysis of the nucleocapsid polymorphism by a supervised classification approach, although interesting and well thought -especially the reference preparation part-, suffer from severe drawbacks that make it difficult to take the author's conclusions as granted.
First the authors should provide evidence of the correctness of the different helical symmetry assignments: this shouldn't be difficult, since the classification provide them with different segment stacks and associated helical symmetry that could be used for refinement to provide high -or medium-resolution maps corresponding to the the different helical symmetries.On top of validating the classification procedure, this would allow the author to merge subtracted particles from different diameter tubes, hence improving the resolution of the local refinements and better characterizing potential lattice deformation (stretching, etc) by 3D classification or 3D variability analysis of the subtracted particles.
We have now calculated new helical and local reconstructions from a segment particle stack selected after supervised classification, which includes segments that classified to the dominant [n 1 =14, n 2 =14] symmetry (19,012 segments selected from the non-flattened and 1% and 2% flattened classes).Compared to the previously calculated helical reconstruction from 4,983 segments selected after 2D classification, we obtained an improved map as evident from the FSC analysis shown in Extended Data Fig. 2A, supporting our approach of selecting segments for a given symmetry by supervised classification.The resolution of the new local reconstruction is similar to the previous one, limited at 3.2 Å as shown by FSC analysis (Extended Data Fig. 2B), indicating that increasing the number of segments (and consequently the number of subparticles) did not further increase the resolution.
We also analyzed in more detail the 3D classification of the subparticle stack.As shown in an additional supplementary figure (Supplementary Fig. 7), we looked at the class partitioning of subparticles derived from either 0% or 2% flattened segments after classification without alignment of the subparticle stack.As one would expect, classes that displayed the larges radial shifts from the helical axis showed a substantial bias towards particles derived from the 2% flattened segments (classes 1, 7 and 8 in Supplementary Fig. 7) This analysis further supports the correct geometry assignment of segments by our supervised classification approach.
Performing refined 3D helical reconstructions for all geometries from the supervised classification would be computationally expensive and we believe it would not serve as an unbiased validation of the supervised classification result as one would again impose the same symmetry as used when the segments were initially classified.Thus, we think that such an analysis is beyond the scope of this work.
To provide evidence of the correct helical symmetries, we performed Fourier-Bessel analysis of the sum of the power spectra for the five most populated non-flattened classes and plotted the amplitude diagrams for the Bessel orders of the n 1 and n 2 diffraction peaks (Supplementary Fig. 6).
Another simple analysis that would strengthen the approach, would be to show the orientation distribution (on-axis and out-of-plane angles), for some representative references (e.g. the 5 most populated without flattening).The distribution is expected to be ~flat for on-axis angles, and gaussian-shaped, centered on 0 (or 90 depending on the convention) for the out-of-plane angles, if the symmetry assignment is correct.If the first proposed approach (calculating the 3D structures corresponding to the different helical symmetries) is beyond the scope of this work on author's point of view, then the authors should provide these plots for validation.
We plotted the distribution of the on-axis (rot), in-plane rotation angles (psi) and out-of-plane angles (tilt) for the five most populated, non-flattened classes (Revision Fig. 1).As expected, the distribution of the on-axis angles is flat, and the distribution of the out-of-plane angles is gaussian-shaped and centered on 90˚.However, we do not believe that these distributions provide support for the correctness of the symmetry assignment.As one can see in the figure provided as attachment to this rebuttal (Revision Fig. 2), where we plotted for the 3,997 segments that classified as non-flattened [n 1 =14, n 2 =14]-symmetry the alignment angles when aligned to other (wrong) 3D references with symmetries of n 1 =12-16 and n 2 =12-16, respectively, the angle distributions look very similar and one wouldn't be able to tell which one is the correct symmetry.We therefore have not included such plots in the revised manuscript.Instead, we generated the average power spectra (after applying the psi angle and calculated the power spectrum) from segments of the five most populated, non-flattened classes and we determined the Bessel orders of n 1 and n 2 in each power spectrum to verify the symmetry of these classes (Supplementary Fig. 6).
For the flattening, to be more conclusive, the authors could show the sum of power spectra of aligned segments corresponding to a particular helical symmetry (e.g. the most abundant), for the least and the most flattened classes.Effects of the flattening should be visible by the stretching of the signal on the layer lines.This is an interesting suggestion and we have now added this analysis to the manuscript (Supplementary Movie 2).
Lines 345-347, the authors state that "A closer inspection of the segments belonging to tubes with [n1=14, n2=14]-symmetry revealed that only approximately 14% of these segments aligned best to the non-flattened 3D reference."Have the authors tried to run refinements before and after removing flattened segments, e.g.keeping up to flattening of 5%, and assess the improvements?On one hand, this would validate the classification based on flattening, and on the other hand integrate this classification procedure in their processing pipeline.
We have now calculated helical and local reconstructions from segments that classified with [n 1 =14, n 2 =14] symmetry (up to and including 2% flattening).The helical reconstruction improved compared to the one that was calculated from a stack obtained after 2D classification as can be seen in the revised Extended Data Fig. 2A and C. We have updated the manuscript and Supplementary Fig. 1 to reflect integration of this protocol in the processing pipeline.
A.4/ Lines 572-587: the authors describe a complicated protocol for refined helical reconstruction, instead of simply using relion_refine with the helical options.Could the authors explain why?If the reason is the loss of metadata (priors on in-plane and out-of-plane, intersegment distance, filament IDs), then the authors should consider re-extracting in Relion using the filament ends coordinates corresponding to their subset of selected segments.
We appreciate the reviewers' questions regarding the complexity of our data processing approach and we are grateful for their call to explain our rationale for all steps during data processing better for clarity.
The complexity of this structure determination required the use of program tools from different software packages.We made sure that all metadata was carried forward when switching from one package to the other (including all the metadata associated with helical reconstructions, such as the filament ID, helical track length, and prior angles).
Briefly, we used cisTEM for 2D classification because its class averages featured more detailed subunits than Relion and Cryosparc.For 3D reconstruction of the two-times binned data, we first tried cisTEM because of how great its 2D classification algorithm worked for our segments.Tim Grant kindly shared an unpublished beta-version with us, but we were unable to generate a helical map.3D reconstruction in Relion yielded maps with slightly flattened secondary structure features in the calculated maps.Helical reconstruction in cryoSPARC (called "helical refinement" in cryoSPARC) resulted in slightly better maps than Relion.Due to the large diameter of the segments, we were dealing with a large box size of 912 pixels for unbinned data.We used cisTEM for particle alignment when working with large box sizes (912 cubic voxels here) because of its speed and limitations due to memory requirements we frequently encountered when using other software packages for alignment.Alignment, reconstruction, and symmetrization are just treated as separate steps in our protocol.In addition, subparticle extraction was essential for local refinement.Unfortunately, subparticle extraction from a movierefine corrected stack is not possible with Relion (only from the original summed images).For the supervised classification approach, we used cisTEM for the following reasons: Global alignment of the 72K segments was very slow in Relion.In addition, we relied heavily on parallelization, which was easier with cisTEM than we Relion or cryoSPARC.At one point, we used 6,000 CPUs simultaneously.Furthermore, helical refinement in cryoSPARC does not (yet?) offer a local symmetry implementation.
Minor points: B.1/ Lines 144-149: "We initially used ModelAngelo […] in Phenix".Most of this paragraph seem more appropriate for the method section.
We agree that the sentence "Real-space refinement and model validation were performed in Phenix." in lines 148-149 is more appropriate for the Methods section and we deleted it from this paragraph.However, we think that reporting the relatively high success rate of automated model building by ModelAngelo (64% sequence identity, 77% sequence similarity) is appropriate for the Results section because it confirms the quality of the reconstruction as opposed to the biased eyes of the human model builder.We now refer to Supplementary Table 1 at the end of the paragraph.
The paragraph was updated to: "We initially used ModelAngelo for model building 45 , where we observed that-without providing an amino-acid sequence-the program was able to output an almost complete trace of the VP39 structure with a high degree of correct amino acid assignments (64% identity, 77% similarity), confirming the visually assessed quality of the reconstruction.We completed the model by manual building in Coot 46 .The first 11 residues of the N terminus and the last 27 residues of the C terminus of VP39 were unresolved in our cryo-EM reconstruction and were not included in the model (Supplementary Table 1)."B.2/ Lines 132-133: "Our reconstruction reveals that individual VP39 subunits pack as dimers that assemble into 14 protofilaments".This is a general statement that does not apply to the entire dataset, it should be more precisely phrased for the readers to understand that it also assembles in other number of protofilaments structures.
We updated the text in lines 132-134 to "In our reconstruction, individual VP39 subunits pack as dimers that assemble into 14 helical strands and together form the central cylindrical structure of the baculoviral nucleocapsid (Fig. 1C)."We hope that this sentence clarifies that the 14 helical strands are only observed in the reconstruction that is described in this section of the manuscript.
We thank the reviewer for highlighting this description as unclear.This is not a typo; C15 is correct here.This dataset is unusually complex in terms of its size and the sample heterogeneity.This complexity made the determination of helical symmetry parameters and the helical reconstruction inherently challenging.When we started with 3D reconstruction, we were not certain yet about the correct rotational symmetry of the segments.At this point, we knew from helical indexing of early 2D class averages that the rotational symmetry is likely C12-C15.The C15 map, which we used as an input model at this step during data processing, looked more detailed than a C14 map that we generated simultaneously in a brute-force approach using the same segments, where we tested for different possible rotational symmetries.This may be due to the fact that the C15 map contained more segments with C15-symmetry than maps, which we generated later.Our selection of 2D classes, which was used to generate the C15 map, was not that precise yet.We did not strictly adhere to the exact same segment diameter for picking 2D classes yet.Instead, we picked all classes that looked alike but may have differed slightly in tube diameter.Latter maps contain fewer segments due to finer selection during 2D classification.However, the C15 map was good enough as a first input model.
We added the following sentence to the manuscript in line 536 for clarification: "Finer selection in these and subsequent rounds of 2D classification, where we focused exclusively on class averages with C14 rotational symmetry, led to switching from C15 to C14 symmetry for helical reconstruction." B.4/ Supplementary Fig 2A: "Power spectrum of a 2D class average, which has been symmetrized along its meridian".Instead of the PS of the 2D class average, it is recommended to use the sum of PS of the segments belonging to that class-average, which avoid some artifacts present in the PS of class-averages, such as left/right asymmetry.No symmetrization should be necessary if the PS is not artifactual.
We thank the reviewer for this comment.We have now calculated the sum of the power spectra of the segments, repeated the helical indexing, and we have now updated Supplementary Fig. 2 in the manuscript with the new power spectra and curves.As the reviewer suggested, no symmetrization was necessary.B.5/ Lines 315-316: "potential symmetries (C12-C15) possible for the given Bessel orders identified during Fourier-Bessel analysis of several 2D class averages (Supplementary Fig. 2)."Supp Fig 2 shows only the analysis on one class, therefore the reader can not appreciate the validity of this statement and the differences in first Bessel peak position across the different structures (which might actually be compensated by diameter variation).
We thank the reviewer for pointing out the benefit of showing the observation of other potential symmetries.We have removed this sentence from the manuscript.These 2D class averages were obtained prior to finer selection during 2D classification and thus may include closely related symmetries in one class average (also see comment B.3). Deducing the correct symmetry at this step is very challenging.B.6/ Lines 544-545 : "We determined initial helical symmetry parameters by indexing the power spectra of these class averages using PyHI (Python v. 3.7)".It is not clear why this indexation was done, since the authors already obtained helical parameters in previous steps.
We appreciate the reviewer's thoroughness and efforts to help us clarify our data processing approach.The scheme in Supplementary Fig. 1 shows the full final data processing approach for the data collections, which resulted in this reconstruction.In this paper, we only discuss data, which we collected on graphene-coated grids.However, prior to using graphene-coated grids, we tried to reconstruct the nucleocapsid with data that we collected from conventional carbon support grids (Quantifoil).The helical parameters, which we used for the extraction of the segments described in this paper, stem from helical indexing of 2D class averages of data collected from the conventional carbon grids.The nucleocapsids for all data collections were prepared using the same virus and same purification protocol.
While we collected a similar number of movies, we observed about five times less tubes on the conventional Quantifoil grids, compared to the graphene-coated grids (16,402 segments were extracted from 45,000 micrographs for conventional Quantifoil grids; 74,600 segments were extracted from 46,000 micrographs of graphene-coated gold grids).The 16K segments were not sufficient to get beyond a blobby low-resolution structure and we were not able to confirm the helical symmetry parameters.
We updated the Results section in line 116 to: "Cryo-EM data collection was greatly facilitated by graphene-supported grids, which increased particle yield per micrograph by a factor of 5 and made this reconstruction possible 42 .With an initial data set collected from conventional Quantifoil grids (16,402 segments from 45,000 micrographs), we were only able to obtain a low-resolution reconstruction.
In addition, we added an explanation to the Methods section in line 526: "The helical symmetry parameters, which were used for segment extraction, were obtained from Fourier-Bessel analysis of 2D class averages of previously collected data of AcMNPV VP39 nucleocapsids on conventional Quantifoil grids (as opposed to graphene-coated gold grids)."B.7/ For the local refinements, it should be stated whether refinement was done with C2 (or D1) symmetry, or only in C1.Since the symmetry expansion was done with C14 and not D14, we would recommend the authors to use the 2-fold symmetry for refinement.
We carried out the local refinement with C1 setting, but applied local symmetry after each iteration, thereby averaging the density of all protomers (8) that were included in the volume.Thus the 2-fold symmetry was used for refinement.We have now written this more clearly in the Methods section.
B.8/ Validation report, section 6.2.1/6.2.2:While the "raw map" seem to have 2-fold cyclic symmetry, or at least have one of its axis (X) aligned with a (maybe imposed, see point B.7 to clarify) C2 symmetry axis, this is not the case for the "primary map".Why such a difference?
The "primary" and "raw" maps were the same, except that the "primary" map was boxed.
In the "raw map" central slices, can the author explain the very strong differences in areas with no protein density near the center and the areas with no protein density far from the center?In other words, why is the noise appearance so different depending on the area of the volume?It looks like a different low-pass filter had been applied in different areas, which seem odd for a "raw map".Good observation.The "raw" map was not an unmodified map (as it should be) and was local symmetry averaged.The noise in the regions where the local symmetry mask was applied (around each protomer) is much lower than on the outside.We have now revised the deposition and uploaded all relevant maps (see also comment above).
Revision Fig. 1 Out-of-plane angles On-axis angles In-plane rotation angles Revision Fig. 2 REVIEWER COMMENTS Reviewer #1 (Remarks to the Author): The authors have done a very good job in addressing my concerns, and in general the paper is now suitable for publicafion.However, I would take excepfion to the argument made here in responding to Reviewer #2 and the inclusion of Supp.Fig. 6 as establishing the correctness of their helical indexing: "To provide evidence of the correct helical symmetries, we performed Fourier-Bessel analysis of the sum of the power spectra for the five most populated non-flaftened classes and plofted the amplitude diagrams for the Bessel orders of the n1 and n2 diffracfion peaks (Supplementary Fig. 6)." The agreement between the layer line intensifies of the projected 3D reconstrucfion and that from the averaged power spectrum of the raw segments is a necessary, but not sufficient, condifion for having used the correct symmetry.This is actually shown in a Methods in Enzymology chapter (Egelman, 2010) where the degeneracy of symmetries is shown and discussed, illustrafing how wrong symmetries (at some finite resolufion) can be indisfinguishable in terms of layer line intensifies.It is stated in the legend for Fig. 6.8 in that chapter: "Despite having different Bessel orders on layer lines 1, 2, 4, and 5, the power spectra all have peaks at idenfical posifions due to the fact that the diffracfion is coming from different radii."At some higher resolufion, one would see a divergence between the reconstrucfion and the raw data, but this resolufion might be significantly beyond what is present in the power spectrum from the raw segments.Thus, the main argument for having used the correct symmetry is producing an interpretable map at high resolufion, and that one symmetry (the correct one) produces a befter map than all other symmetries possible.An example was published (Zheng et al., 2020) where at 5 Å resolufion two different symmetries produced indisfinguishable volumes, and thus would have had indisfinguishable power spectra.However, the correct symmetry led to a 3.9 Å map, while the incorrect symmetry never improved beyond 5 Å.

Reviewer #2 (Remarks to the Author):
In the reviewed version of their arficle "Helical reconstrucfion of VP39 baculovirus nucleocapsid assembly reveals principles for baculovirus nucleocapsid assembly", the authors have addressed a number of points of concern, including technical errors that lead to the inflafion in their FSC curves, performed new validafions of their classificafion procedure, as well as slightly adapted some steps of their processing strategy.The authors have added new supplementary figures and corrected their text based on reviewers comments.While this improved manuscript seem suitable for publicafion (with a minor correcfion proposed), and the detailed explanafions were highly appreciated, some of the point-to-point answers require comments, as followed.
Minor correcfion : the middle panels in supplementary fig.7 (AnglePsi) do not seem to add anything to the analysis of the classificafion, and is proposed to be removed.Indeed, those angles are random and not linked to any geometrical considerafions, unlike the AngleRot or AngleTilt.
Comments on the point-to-point answers : "Performing refined 3D helical reconstrucfions for all geometries from the supervised classificafion would be computafionally expensive and we believe it would not serve as an unbiased validafion of the supervised classificafion result as one would again impose the same symmetry as used when the segments were inifially classified.Thus, we think that such an analysis is beyond the scope of this work." The authors have performed addifional helical and local reconstrucfions for the 14,14 symmetry (which contain the most segments and hence will take longer to compute) in the reviewing process, the argument of the processing fime seems therefore unjusfified.The fact that the same symmetry as used for the classificafion procedure is imposed is not a problem : the validafion would come from the fact that the obtained reconstrucfions are correct and at high resolufion (which would be only true if the correct symmetry has been imposed).
"We plofted the distribufion of the on-axis (rot), in-plane rotafion angles (psi) and out-of-plane angles (filt) for the five most populated, non-flaftened classes (Revision Fig. 1).As expected, the distribufion of the on-axis angles is flat, and the distribufion of the out-of-plane angles is gaussian-shaped and centered on 90." Unlike stated, the distribufion of the on-axis angles is only flat for the 14,14 map, but not for the 13,14 (although nearly ok) and really not for the 15,14 map, while the other symmetries have too few segments to judge.Together with the not always well fifting data/predicted PS as shown in the new supplementary figure 6, and with the fact that the authors have not calculated helical reconstrucfion for those other symmetries, there is a remaining doubt about the correctness of the symmetry assignments based on the reference based classificafion approach.
"As one can see in the figure provided as aftachment to this rebuftal (Revision Fig. 2), where we plofted for the 3,997 segments that classified as non-flaftened [n1=14, n2=14]-symmetry the alignment angles when aligned to other (wrong) 3D references with symmetries of n1=12-16 and n2=12-16, respecfively, the angle distribufions look very similar and one wouldn't be able to tell which one is the correct symmetry." For the AngleRot plots (which are the most interesfing ones, when it comes to detecfing wrong symmetry imposed), the fact that the distribufion is not even when the correct symmetry is imposed (unlike what is shown in Revision Fig. 1, why ?) is a problem and may indicate wrong translafional search range parameters (which should be limited to +/-half the axial rise in Y).Indeed, in those condifions, it is hard to judge the correctness of the maps from the AngleRot plots, but the authors should be aware that these are often useful indicafions (and should maybe make them worry about the 15,14 map plots shown in Revision Fig 1).

EDITOR COMMENTS
You will see that, while the reviewers find that your revisions improved the manuscript, some important points remain to be addressed.Please ensure all requests are undertaken including calculation of helical reconstructions for the symmetries that they are excluding as possible fits and the inclusion of a Supplementary Figure to further explore this area.

REVIEWER COMMENTS
Reviewer #1 (Remarks to the Author): The authors have done a very good job in addressing my concerns, and in general the paper is now suitable for publication.However, I would take exception to the argument made here in responding to Reviewer #2 and the inclusion of Supp.Fig. 6 as establishing the correctness of their helical indexing: "To provide evidence of the correct helical symmetries, we performed Fourier-Bessel analysis of the sum of the power spectra for the five most populated non-flattened classes and plotted the amplitude diagrams for the Bessel orders of the n1 and n2 diffraction peaks (Supplementary Fig. 6)." The agreement between the layer line intensities of the projected 3D reconstruction and that from the averaged power spectrum of the raw segments is a necessary, but not sufficient, condition for having used the correct symmetry.This is actually shown in a Methods in Enzymology chapter (Egelman, 2010) where the degeneracy of symmetries is shown and discussed, illustrating how wrong symmetries (at some finite resolution) can be indistinguishable in terms of layer line intensities.It is stated in the legend for Fig. 6.8 in that chapter: "Despite having different Bessel orders on layer lines 1, 2, 4, and 5, the power spectra all have peaks at identical positions due to the fact that the diffraction is coming from different radii."At some higher resolution, one would see a divergence between the reconstruction and the raw data, but this resolution might be significantly beyond what is present in the power spectrum from the raw segments.Thus, the main argument for having used the correct symmetry is producing an interpretable map at high resolution, and that one symmetry (the correct one) produces a better map than all other symmetries possible.An example was published (Zheng et al., 2020) where at 5 Å resolution two different symmetries produced indistinguishable volumes, and thus would have had indistinguishable power spectra.However, the correct symmetry led to a 3.9 Å map, while the incorrect symmetry never improved beyond 5 Å.
We agree with the Reviewer that an interpretable map at high resolution is the main argument to confirm correctness of the symmetry assignment, as we have done for our main [14,14]symmetric reconstruction (3.6 Å resolution of the helical reconstruction).Indeed, our analysis produced a map where ModelAngelo was able to build an almost complete model, with a high degree of confidence in placing the correct amino acids without providing an amino acid sequence (as described in lines 153-157).The final fit of our model, with correct stereochemistry and validated, fits into the map as one would expect.
We have now calculated reconstructions from segments that partition into classes with helical symmetries other than [14,14] after supervised classification, as summarized in Supplementary Fig. 8 and Supplementary Table 5. See comment below to Reviewer #2.
We agree with the Reviewer that "the agreement between the layer line intensities of the projected 3D reconstruction and that from the averaged power spectrum" may not be a sufficient condition for having used the correct symmetry.In fact, the correct interpretation of the power spectra from these assemblies is extremely complicated (e.g., if the helical repeat distance is very large, the selection rule becomes complicated, resulting in many layer lines).In order to not rely on Fourier-Bessel indexing, we have completely revised Supplementary Fig. 6.It now shows directly the fit between the power spectra of the five most populated, non-flattened classes and back-projections of the 3D references they classified with, without relying on Fourier-Bessel indexing.In panel A, we show the averaged power spectra of the segments after applying the psi alignment angle.In panel B, we show the averaged power spectra calculated from reference projections after orienting them with the same alignment parameters as the corresponding observed segments.Panel C shows the layer line profiles for prominent layer lines (observed vs calculated) for each class without indexing.We also made Supplementary Movie 3 (comparison between observed and calculated power spectra) and Supplementary Movie 4 (comparison of the power spectra from different symmetries).We also added an extra sentence in line 359 in the results section: "The imposed symmetries for segments partitioning into 3D references are consistent when comparing the direct fit of averaged power spectra of calculated and observed segments (Supplementary Fig. 6, Supplementary Movies 3 and 4).Given the caveats associated with analyzing Fourier spectra 57,58 , interpretable maps would be the best way to verify correct helical symmetry assignments.However, while we calculated reconstructions for segments of the three most populated, 0-2% flattened classes (Supplementary Fig. 8), we did not have a sufficiently high number of segments to yield an interpretable map to unambiguously prove the correct helical symmetry assignments for symmetries other than our [14,14] 1321-1328.e2 (2020).
Reviewer #2 (Remarks to the Author): In the reviewed version of their article "Helical reconstruction of VP39 baculovirus nucleocapsid assembly reveals principles for baculovirus nucleocapsid assembly", the authors have addressed a number of points of concern, including technical errors that lead to the inflation in their FSC curves, performed new validations of their classification procedure, as well as slightly adapted some steps of their processing strategy.The authors have added new supplementary figures and corrected their text based on reviewers comments.While this improved manuscript seem suitable for publication (with a minor correction proposed), and the detailed explanations were highly appreciated, some of the point-to-point answers require comments, as followed.
Minor correction: the middle panels in supplementary fig.7 (AnglePsi) do not seem to add anything to the analysis of the classification, and is proposed to be removed.Indeed, those angles are random and not linked to any geometrical considerations, unlike the AngleRot or AngleTilt.
We have revised the old Supplementary Fig. 7 as suggested by removing the AnglePsi distribution plots.
Comments on the point-to-point answers: "Performing refined 3D helical reconstructions for all geometries from the supervised classification would be computationally expensive and we believe it would not serve as an unbiased validation of the supervised classification result as one would again impose the same symmetry as used when the segments were initially classified.Thus, we think that such an analysis is beyond the scope of this work." The authors have performed additional helical and local reconstructions for the 14,14 symmetry (which contain the most segments and hence will take longer to compute) in the reviewing process, the argument of the processing time seems therefore unjustified.The fact that the same symmetry as used for the classification procedure is imposed is not a problem: the validation would come from the fact that the obtained reconstructions are correct and at high resolution (which would be only true if the correct symmetry has been imposed).
The main difference in processing time between calculating a [14,14]-symmetric reconstruction, and one without rotational symmetry, e.g.[13,14], stems from the fact that the later requires map symmetrization by applying local symmetry (which is slower) instead of applying point-group symmetry.We have now implemented local symmetry calculation for map symmetrization and calculated helical reconstructions for the most populated classes after supervised classification.The result is summarized in a new Supplementary Table 5.It shows that the resolution obtained for the [13,14] and [15,14] symmetries is comparable to the resolution obtained for a [14,14] reconstruction calculated from a similar number of segments, and thus consistent.But one can also see that limiting the number of segments to about 1200 does not yield high-resolution reconstructions, even for the [14,14] class.Therefore, we do not have a sufficient number of segments to unambiguously prove the correctness of the symmetry assignment for the other classes.We have added a sentence in the results section explaining this limitation in line 359 and a description in the methods section starting in line 693.
"We plotted the distribution of the on-axis (rot), in-plane rotation angles (psi) and out-of-plane angles (tilt) for the five most populated, non-flattened classes (Revision Fig. 1).As expected, the distribution of the on-axis angles is flat, and the distribution of the out-of-plane angles is gaussian-shaped and centered on 90˚."Unlike stated, the distribution of the on-axis angles is only flat for the 14,14 map, but not for the 13,14 (although nearly ok) and really not for the 15,14 map, while the other symmetries have too few segments to judge.Together with the not always well fitting data/predicted PS as shown in the new supplementary figure 6, and with the fact that the authors have not calculated helical reconstruction for those other symmetries, there is a remaining doubt about the correctness of the symmetry assignments based on the reference based classification approach.
We have revised Revision Fig. 1 and 2, where we correctly account now for the redundancy of AngRot angles for any given helical symmetry.The distributions of the AngRot angles are flat for all helical symmetries in Revision Fig. 1 and 2 (where there are enough segments to obtain a representative distribution).Please see response to last comment for explanation and revision of the figures.
We have completely revised Supplementary Fig. 6 in order to show directly the fit between the power spectra without relying on Fourier-Bessel indexing by the PyHI program.The analysis is still for the same five most populated helical symmetries.In panel A, we show the averaged power spectra of the segments after rotating the segments according to the psi angle from the 3D alignment.In panel B, we show the averaged power spectra calculated from reference projections after orienting them with the same alignment parameters as observed for each segment and applying the psi alignment angle.Panel C shows the layer line profiles for prominent layer lines (observed vs calculated) for each helical symmetry.We have also added Supplementary Movie 3 that shows the fit between the observed and calculated averaged power spectra for the five most populated helical symmetries, and Supplementary Movie 4 that shows the difference between the power spectra from different helical symmetries.As can be seen in Supplementary Fig. 6 and Supplementary Movie 3, the observed and calculated power spectra agree well, supporting the correctness of the supervised classification result.
"As one can see in the figure provided as attachment to this rebuttal (Revision Fig. 2), where we plotted for the 3,997 segments that classified as non-flattened [n1=14, n2=14]-symmetry the alignment angles when aligned to other (wrong) 3D references with symmetries of n1=12-16 and n2=12-16, respectively, the angle distributions look very similar and one wouldn't be able to tell which one is the correct symmetry."For the AngleRot plots (which are the most interesting ones, when it comes to detecting wrong symmetry imposed), the fact that the distribution is not even when the correct symmetry is imposed (unlike what is shown in Revision Fig. 1, why ?) is a problem and may indicate wrong translational search range parameters (which should be limited to +/-half the axial rise in Y).Indeed, in those conditions, it is hard to judge the correctness of the maps from the AngleRot plots, but the authors should be aware that these are often useful indications (and should maybe make them worry about the 15,14 map plots shown in Revision Fig 1).
We have revised Revision Fig. 1 and 2 to represent the true unbiased AngleRot distribution.For the AngleRot plots, the distributions are in fact even or random (as one, including Reviewer #2, would expect).Because of helical symmetry, there are redundant and equivalent (e.g.giving an identical alignment score) alignment angles and shifts for each segment, when the alignment is carried out in C1 (as we did) against non-flattened references.Which one of these equivalent solutions the alignment program reports might be random or not (as it appears to be the case of cisTEM used here).
In order to represent the true unbiased AngleRot distribution, we must account for the redundancy of AngleRot angles, depending on the helical symmetry, between 0 and 360 degrees before plotting the distributions.For this, we used the following python code before plotting the distributions, where twist1 and twist2 are the helical twists associated with the symmetry defined by n1 and n2: The revised distribution plots are shown in Revision Fig. 1_revision_02 and 2_ revision_02.As one can see, the distributions look even for all symmetries.Thus, we believe that there is no indication for wrong translational search range parameters or incorrectness of the maps.
We have updated Supplementary Fig. 7 by applying the above code before plotting the AngleRot distributions.
In the previous revision, we only accounted for this with the rotational symmetry in case of the [14,14] assembly in Revision Fig. 1, but not in the plots of Revision Fig. 2, which is why they looked different.